{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "K-means clustering - lab solution\n",
    "----"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pylab as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Geneate some data with three clear clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "cluster_means = [[0,0],[4,4],[-4,4]]\n",
    "n_data = 20 # Number in each cluster\n",
    "x = np.empty(shape=(0,2))\n",
    "for i,m in enumerate(cluster_means):\n",
    "    x = np.vstack((x,np.random.randn(n_data,2) + np.tile(m,(n_data,1))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10aefaf10>]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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7DzRaPIj0iHJLEQCsl+VDzaKs6liLUwvRljC2+VBhEMBmqj3nTh09nDRxTcESBtCWTtUF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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ac15f10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(x[:,0],x[:,1],'ro')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initialise the things needed for k-means"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# set K\n",
    "K = 3\n",
    "# Initialise the means\n",
    "mu = np.random.randn(K,2)\n",
    "# Set maximum number of iterations\n",
    "max_its = 20\n",
    "N = len(x)\n",
    "z = np.zeros((N,K))\n",
    "oldz = np.ones((N,K)) # just to make sure it is different from z in iteration 1\n",
    "\n",
    "# Colours for plotting - if you set K bigger than the \n",
    "# length of this, it'll crash\n",
    "cols = ['ro','bo','go','yo','mo','ko']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run the algorithm - plotting the state at each iteration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Mw+6lRiMDIpMI0uplkShRIOAvBQMSeH5fkMNUiUxEZCo0TSCBVKwc5WGrRCYiMhUaGZDA\nGb0gdz3XxVDjEPvP3s9Q4xBdv+2ipr7G0zv0UkqJKiJSKAoGJHCKeUEutZSoIiKFoGBAAqdYF+RS\nTIkqIlIICgYkUIp5QS7FlKgicrzpfD9EPchXMCCBUuwLctgqkYlExXR2AWnn0FHaTSCBU4gc5dNN\nWNKxtoMd9TtI2mSm/exuAmdvNiXq7cFOiSoSRdPZBaSdQ+NpZEACZ7o5ygsR5SslqkjpyXfRsbVW\nO4eOYYI0T2KMqQIGBgYGqKqqKnZ3pIhSqRRt7W30bO8h7aSJuTEa6xppb2vPeUEeF+WPvaPf55B4\nJjHtC7lSoooEX2VVJUONQ7nXGlmo6K3gJ4/8ZFzukt8++1uOrD4y6XsGBwY97nlh7d69m+rqaoBq\na+3ufN6raQIJpHxzlI+L8keNRvk2E+V33tSZdz/8CAQUcIhM31QWHR82h3n/We/n52/5eWZKAOB+\nprRQOSqfTU0TSOBN5cNYavkBtHBJpDCmsuj4vw78VyYQGJ0SMMAf0c6hMRQMSMkrtfwAxcywKBJG\nJ9oFxBGOv1l4E7An9/GiuHNIwYCUvGJvR8yXFi6JFNaJFh2fUn7K8TcLfw30A8+Q10LlsFIwIK8K\nyp3zdJRSfoBSm9IQCboT7QI6mZOPv1k4GbgA+DWcdOdJkd85pAWEEZdKpdjQ2kpfby9l6TQjsRi1\nDQ1c1+FtdcBCK5X8APlMaQRlJEOkFEy26HjC3CUng7PI4X++73/y2c98NtKfOY0MRFgqlWJVTQ01\nXV1sGxrim/v3s21oiJquLlbVlNbcdankByi1KQ2RUnTs52cquUui/plTMBBhG1pbuSaZZKXrjp26\nZqXrsiaZ5Oa20pq7Hr0zGBwY5Nknn2VwYJDOmzoDEwiMKqUpDZEwKJWbhWJS0qEIq6usZNvQ0EQ5\nN6ivqGDbYGkl3SgFEyZIyk5p6MtJxFszmYYL8hTeTJIOaWQgoqy1lKXTk01dMzcdnO14YaK7FJHi\nyvdiHoW8IFpAGFHGGEZiMSwTZuNkJKa5a6/km2FRRIojKgWNNDIQYbUNDWxxcv8JPOw4LG3U3LUf\nFAiIBFdU8oJ4GgwYY1YbY35sjDmY/XnCGLPSyzZl6q7r6OCWRIKHHGfsAlsechw2JhJc2x6M7Xgi\nIsUSlbwgXo8MPAv8M1Cd/dkBfNMYk/C4XZmCeDzO5v5+djU3U19RwTkLF1JfUcGu5mY294dj6EtE\nZLpKLdX5THi6ZsBa++1jHmozxlwFvB9Ietm2TE08Hmd9Zyd0+jN3rflxESkV4/KCTLC4Kix5QXxb\nM2CMcYwxFwJzyWSEloDx6g86lUrR0rKOyso6Fi06l8rKOlpa1oVqJa6IhFNU8oJ4vpvAGHMGmYv/\nbCAFfNBa+3Ov2w27UrnDTqVS1NSsIpm8Btddz+hS3K6uLezYsYr+/s2ajhCRwCqVVOcz5cfIwM+B\ndwPvAz4PfMkY83Yf2g2dVCrFupYW6iorOXfRIuoqK1nXEuy9rq2tG7KBwErGLsV13ZUkk2toa7u5\nmN0TEZlUVPKC+J6B0BizDdhjrb0qx3NVwMCyZcuYN2/euOeamppoamryqZeFN9M7+dE6Atckk6zI\npg+2wBbH4ZZEIrAL/ior6xga2sZEE24VFfUMDm7zu1siItMSlFHZ7u5uuru7xz128OBBdu7cCdPI\nQFiMpEMOmeKRE9q4cWMo0hEXsiLg2DoCo0brCNhsHYH1nZ0F/g1mxlpLOl3GZEtx0+m5gflwiYic\nSFC+q3LdII9JR5w3r/MMdBhjlhpj3myMOcMY82lgOfAVL9sNgkJXBOzr7WWFm3uv60rXpa8neHtd\njTHEYiNMVqIvFhsJzIdLRKQUFWKE3+s1A68HvkRm3cB2MrkG6q21Ozxut+gKWRGwlOsINDTU4jhb\ncj7nOA/T2LjU5x6JSNAE8bsr6HLVS/i3zn+b9vG8zjNwuZfHD7K+3l7WT3Inf0tPD0xxWL+U6wh0\ndFzHjh2rSCbtmEWEFsd5mERiI+3tm4vdRREpglQqReuNrfRu7yU9K03sSIyGugY61uY/jRo1E9VL\n+OX3fzntY6o2gQe8uJMv1ToC8Xic/v7NNDfvoqKinoULz6Giop7m5l3aVigSUaMXs67nuhhqHGL/\n2fsZahyi67dd1NTnP40aNRPVS7BvnP4Ii6oWesCLO/nrOjpYtWMHdszUgyUTCGxMJNgc4DoC8Xic\nzs71dHYGZyWuiBTPuIvZqNHiPzZT/KfzpmAtiA6S3u29mRGBAtLIgEcKfScfljoCCgREJCrFf7xw\nwnoJ06SRAY94cSfvdx0BEZFCy6f4j77jjnfCegnTpJEBj3h9J68PiYiUonEXs1xCVPzHK5PVS5gu\njQx4SHfyIiLHa6hroGtfV86pgjAV//HKRPUSzLMGO2GUNTmNDPhEgYCISEbH2g4SzyRw9jhHRwgs\nOHuyxX/agrsgOggmqpdwwesumPYxfa9NMJnR2gQDAwOhSEcsIiK5pVIp2trb6NneQ9pJE3NjNNY1\n0t7WXjILooNidOR5TDrikqhNICIiERePx+m8qZNONI06U4U4d5omEBGRolIgUHwKBkRERCJOwYCI\niEjEKRgQERGJOAUDIiIiEadgQEREJOIUDIiIiEScggEREZGIUzAgIiIScQoGREREIk7BgEhABalu\niIiEm4IBkQBJpVK0XN9CZVUli967iMqqSlqubyGVShW7ayISYipUJBIQqVSKmvoakkuSuI1Ha5R3\n7etiR/0O+rf2q5qbiHhCIwMiAdF6Y2smEFiSDQQADLiLXZJLkrS1txW1fyJRE6WpOgUDIgHRu70X\nd7Gb8zl3sUvP9h6feyQSPVGdqtM0gUgAWGtJz0ofHRE4loG0k1bddxEPRXmqTiMDERelYbAgM8YQ\nOxKDif45LMSOxBQIiHgoylN1CgYiKJVKsa6lhbrKSs5dtIi6ykrWtYR/GCzoGuoacPbl/kg6ex0a\nz2r0uUci0RLlqToFAxGTSqVYVVNDTVcX24aG+Ob+/WwbGqKmq4tVNTUKCIqoY20HiWcSOHucoyME\nFpw9Dok9Cdrb2ovaP5Ewy2eqLow8DQaMMTcYY540xvzBGPM7Y8yDxpi3etmmTG5DayvXJJOsdN2x\no2CsdF3WJJPc3BbeYbCgi8fj9G/tp3lBMxW9FSz81kIqeitoXtAc6rlKkSCI+lSd1yMDZwK3Ae8D\n6oAYsNUYM8fjdmUCfb29rHBzD4OtdF36esI7DFYK4vE4nTd1MjgwyLNPPsvgwCCdN3UqEBDxQZSn\n6jwNBqy1/5e19svW2qS19qfApcCbgGov25XcrLWUpdOTjYIxNx3eYbBSE9Y7EJGgivJUnd9rBk4l\nc4pf9LldIXNxGYnFJhsFYyQW3mEwEZHJRHmqzrc8AyZzhfks8Li19md+tSvj1TY0sKWri5U5pgoe\ndhyWNoZ3GExE5ERGp+o66YxUXg/j15CwMebzwAqg1lr73ASvqQIGli1bxrx588Y919TURFNTk/cd\nDbnR3QRrxiwitGQCgY2JBJv7wx39ioiEQXd3N93d3eMeO3jwIDt37gSottbuzud4vgQDxpjPAQ3A\nmdbaX03yuipgYGBggKqqKs/7FVWpVIqb29ro6+lhbjrNy7EYtY2NXNverkBARKRE7d69m+rqaphG\nMOD5NEE2EDgHWD5ZICD+icfjrO/shM5oDYOJiEhungYDxpjbgSagERgxxrw++9RBa+0rXrYtU6NA\nQEREvN5NsBr4c+AR4Ddjfj7kcbsiIiIyRZ6ODFhrle5YREQk4HSxFhERiTgFAyIickLKTBpuCgZE\nRCSnVCpFy/UtVFZVsui9i6isqqTlepU7DyPfMhCKiEjpSKVS1NTXkFySxG10Gc1Q1rWvix31O0Kf\nnjdqNDIgIiLHab2xNRMILMkGAgAG3MUuySVJ2tpV7jxMNDIgIpKVTCZ57InH2Pb4NvYO7sW1Lo5x\nWFy5mLOWnsWZf30miUSi2N30Re/23syIQA7uYpee3h466fS5V+IVBQMiEmmHDh3ini/fw21338aB\nuQcYLh/GfYMLf8OrQ+M//P0PeWDrA5TfV878l+dz9ceu5tKPXMqcOXOK3HtvWGtJz0ozWb3ztJNW\nBtMQ0TSBiETWozsf5YzaM1izdQ3JDyR5ftnzuO9w4bWMGxrnteC+w+X5Zc+T/ECSNVvXcMbSM3h0\n56NF7L13jDHEjsSYrN557IjKnYeJggERiRzXdbnyk1dyftv57Fuxj8PvPAyxKb45BoffeZh99fs4\nv/V8rvzklbg5SoKXuoa6Bpx9uS8Rzl6HxrNU7jxMFAyISKS4rsv5Hz2f+359H8MfGIbZ0zzQbBiu\nG+a+X9/H+R89P3QBQcfaDhLPJHD2OEdHCCw4exwSexK0t7UXtX9SWAoGRCRSVq9ZzdZDWxl510hB\njjfyrhG2HtrKVddcVZDjBUU8Hqd/az/NC5qp6K1g4bcWUtFbQfOCZm0rDCEtIBSRyHjk0Ud4cPeD\njNQVJhAYNfKuER7Y/gAf3vlhli9bXtBjF1M8Hqfzpk46UbnzsNPIgIhEwqFDh/j4mo8zvHTYk+MP\n1w5z2ZrLOHTokCfHLzYFAuGmYEBEIuGeL9/D/tP3T3+NwInMgd9U/oZ7v3KvRw2IeEfBgIhEwm13\n38bhtx/2tI1X3v4Kt37xVk/bEPGCggERCb1kMsmBuQemvn1wumJwYO4Bksmkxw2JFJaCAREJvcee\neIwX5r/gS1vD84fp6+/zpS2RQlEwICKht+3xbdi/mCidXmG5b3DZ+vhWX9oSKRQFAyISensH98Jr\nfGrstbB3316fGhMpDAUDIhJ6rnUnLrpTaCbbnkgJUTAgIqHnGGfiojuFZrPtiZQQ/cWKSOgtrlwM\nv/epsRdh8emLfWpMpDAUDIhI6J219CzMc/7MEzi/dahfWu9LWyKFomBAREJvac1SXnfgdb60VX6g\nnNqaWl/aEikUFSoSKSFeFosJWyGaVCpF642t9G7vJT0rze9/9XuowdvEQ2mY//J8EomEh42IFJ6C\nAZGAS6VStLZuoLe3j3S6jFhshIaGWjo6rptxGVkvj11MqVSKmvoakkuSuI3ZnQS7gZ8CVd61O/vn\ns2m5rMW7BkQ8omBAJMBSqRQ1NatIJq/BddeTuapZurq2sGPHKvr7N0/7ou3lsYut9cbWTCCwZMwW\nv3cCXwXegTfFig7BgsEFXHLxJXm9LWwjMlKatGZAJMBaWzdkL9YrObpR3uC6K0km19DWdnMgjz2W\ntX7t6Tuqd3sv7uJj9vrHgL8FtnjTZnlfOXd/9m7mzJlzwtemUilarm+hsqqSRe9dRGVVJS3Xt5BK\npbzpnMgJeBoMGGPONMb0GGP2G2NcY0yjl+2JhE1vbx+uuyLnc667kp6e6efA9/LYqVSKlpZ1VFbW\nsWjRuVRW1tHSss6Xi521lvSsdO4kQ28GysDsKuydeNlPyjiv+jyWnbnshK8dncLoeq6LocYh9p+9\nn6HGIbp+20VNfY0CAikKr0cGyoAfAZ/Av5QfIqFgrSWdLmPi1HmGdHrutO68vTz26PRDV1cNQ0Pb\n2L//mwwNbaOrq4aamlWeX+yMMcSOxCb+xvk7mP2j2ZT9pKwg7ZX9pIz6OfV8/pbPT+n146Ywjg7I\n4C52SS5J0tbeVpB+ieTD02DAWvuwtfZfrLXfwL9koCKhYIwhFhth4quaJRYbmdZ8s5fH9mv6YTIN\ndQ04+3J/vTn7HC6/+HIuWnQR5dvL4ZVpNnIIyreXc/GbLmbTlzbhOFP7Os05hZHlLnbp2d4zzQ6J\nTJ/WDIgEWENDLY6Te5LbcR6msXFp4I7t5fTDVHWs7SDxTAJnz5g0xBacPQ6JPQk61nZw52fvZFPH\nJk7fcjqzfzob0lM8eBpm/3Q2p287nU0dm7hj4x1TDgQmncIAMJB20kVZZyHRpmBAJMA6Oq4jkbgF\nx3mIsVc1x3mIRGIj7e3XBurYXk4/5CMej9O/tZ/mBc1U9Faw8FsLqeitoHlBM/1b+1/dJbF82XKe\n6nuKjSs2kvhugtN2nobznw4cYFwQwQFw/tPhtJ2n8Y4d72Djio089fhTLF+2PK9+nXAKw0LsSEy7\nC8R3xq+Z1FJ4AAAZ+klEQVQI1BjjAudaayccAzPGVAEDy5YtY968eeOea2pqoqmpyeNeigRPKpWi\nre1menr6SKfnEou9TGNjLe3t1xYkz0Chj11ZWcfQ0DZyBwSWioqzGBzcPqN+52uq2/eSySR9/X1s\nfXwre/ftxbUujnFYfPpi6pfWU1tTO+OEQi3Xt9D1266cUwXOHofmBc103tQ5ozYk/Lq7u+nu7h73\n2MGDB9m5cydAtbV2dz7HC2QwMDAwQFWVh5lBREpUKWQgbGlZR1dXTXbNwHiO8xDNzbvo7Fw/43ZK\ndX/+uIRIi93R9A44ezNTGGNHLkTysXv3bqqrq2EawYCmCURKiJcXv0Id28upjWJuWSyUqU5hiPjJ\n05EBY0wZsISjyUCvAf4DeNFa+2yO12tkQCQEvJh+GJ8xcQWjt9SOs4VE4paSzZhYqiMcEjwzGRnw\nOhhYTubif2wj91prL8vxegUDIiFTatMPIqUqsNME1tpHrbWOtXbWMT/HBQIiEk6FuuvNZ8uituaJ\n5EdrBkQk8KayZfHw4T9Tvn+RaVLVQhEJvPEZE3MFBH9g+PCjdD338NGSxRa69nWxo36HFuaJnIBG\nBkSkJEyWMZHZHyH99yPK9y8yTQoGRKQkTLZlMTZva2bfUg7K9y9yYgoGRKQkxONx+vs309y8i4qK\nehYuPIeKino+8YnvUf7G1yjfv8gMaM2AiJSMeDxOZ+d6OjvHb1nsrfrSxMsJPMr3r/wAEiYaGRCR\nkjT2QjxpyeK9Do1nNRakzVQqpR0LEkoaGRCRktextoMd9TtI2tz5/ttvb59xG+NqCmjHgoSMRgZE\npOT5ke+/9cbWTCCgHQsSQr5VLZwKpSMWkULwYj6/sqqSocahCdclVPRWMDgwWNA2RfIR2HTEIiLF\n4MViwfSstHYsSGgpGBAROQFjDLEjseNLro3yaMeCiF8UDIiITIFfOxZEikHBgIjIGBMN9Xes7SDx\nTAJnjzM2ASLOnuyOhbaZ71gQKRYFAyISealUipaWdVRW1rFo0blUVtbR0rJuXP4AP3YsiBSLdhOI\nSKSlUilqalaRTF6D665gNIGA42whkbiF/v7NOS/0ykAoQaPdBCIi09TauiEbCKxkbAIB111JMrmG\ntrabc75PgYCEiYIBEYm03t6+7IjA8Vx3JT09fT73SMR/CgZEJLKstaTTZUyWQCCdnqv8ARJ6qk0g\nIoGWTCZ57LFdbNs2wN69v8R1wXFg8eI3c9ZZ1Zx55vtIJBLTOrYxhlhshMlKHsZiI5oSkNBTMCAi\ngXPo0CHuued+brvtaxw48DaGh2tx3X8CTmd0gd8Pf7iPBx4YoLz8DubPf5qrr76ASy+9kDlz5uTV\nVkNDLV1dW7JrBsZznIdpbFxakN9JJMg0TSAigfLoo49zxhn/wJo1hmTyQZ5/vhPX/RCwmHEVgliM\n636I55/vJJl8kDVr4IwzzubRRx/Pq72OjutIJG7BcR5ibAIBx3mIRGIj7e3XFux3EwkqBQMiEgiu\n63LllTdw/vlfYt++Bzl8+FJgqnf5czh8+GPs2/cA559/L1deeQOu607pnfF4nP7+zTQ376Kiop6F\nC8+hoqKe5uZdE24rFAkb5RkQkaJzXZfzz1/N1q3vYWTkihkfr6zsLurrv8+mTXfgOPnd8yh/gJQq\n5RkQkZK2enVrwQIBgJGRK9i69T1cdVVb3u9VICBRpGBARIrqkUce48EHhwsWCIwaGbmCBx54Pu81\nBCJRpGBARIrm0KFDfPzj6xge3uDJ8YeHN3DZZf/CoUOHPDm+SFgoGBCRornnnvvZv/+jwDyPWjiV\n3/zmI9x779c8Or5IOPgSDBhjPmGMGTTGHDLGfM8Y8x4/2hWRYLvttq9x+PAFnrbxyisXcuut93va\nhkip8zwYMMZcANwMrAP+O/BjYIsxptzrtkUkOI7duZRMJjlw4G1MffvgdM3hwIG3kkwmPW5HpHT5\nMTKwBrjTWvsla+3PgdXAy8BlPrQtIkWUSqVoaVlHZWUdixadS2VlHS0t60ilUjz22C5eeKHWl34M\nD9fS1/ekL22JlCJPgwFjTAyoBr47+pjN3B5sB2q8bFskKoKUK2SsVCpFTc0qurpqGBraxv7932Ro\naBtdXTXU1KziO9/5HtZW+9IX161m69YBX9oSKUVejwyUA7OA3x3z+O+AN3jctkhopVIp1rW0UFdZ\nybmLFlFXWcm6lhZSqVSxu/aq1tYNJJPXZHP+H00j7LorSSbX8MQTA2RqDfhhMXv3Do17JKhBlEgx\nFKtQUabSyATWrFnDvHnjVxc3NTXR1NTkdb9EAi+VSrGqpoZrkknWu+6rH6YtXV2s2rGDzf39gUih\n29vbh+uuz/mc667kpZeuY+LSwYVmcN3MuWtt3UBvbx/pdBmx2AgNDbV0dFwXiHMmMlXd3d10d3eP\ne+zgwYPTPp6n6Yiz0wQvA6ustT1jHr8HmGet/eAxr1c6YpETWNfSQk1XFytz5N5/yHHY1dzM+s7O\nIvTsKGstixady/7935zwNbHYfyOdfgp/AgLLu999Nn/6Uzo7WrGC0XsSx9lCInGL6hBIyQtsOmJr\nbRoYAD4w+pjJ5Pr8APCEl22LhFVfby8rJijCs9J16evpyfmcn4wxxGIjTDwAaInFZgH7fOrRXkZG\nDk06bdHWdvOUjqTpBQkjP3YT3AJcaYz5qDHm7cAdwFzgHh/aFgkVay1l6fSE99IGmJtOB+KC1dBQ\ni+Nsyfmc4zzM+9+/BGP8WdTnOAO8+OJwdkTgeK67kp6evgnfP9muCJEw8DwYsNZ+HbgW+BTwQ+Bd\nwApr7Qtety0SNsYYRmKxSe63YSQWC0Sxnf/1v/4H80/9v4Fejo4QWBznOyQSG7nppv/N61438QW4\nkMrLH+ekk8qZeErCkE7PzRlEnWhXhAICCQNfMhBaa2+31lZYa+dYa2ustT/wo12RMKptaGDLBGV5\nH3YcljY2+tyj46VSKS6tr+eO3/8nLXyECt7CQqp5PW9h4alXs3XrPfzVX/0V8+c/DXhdN+AQ8+c/\nw9y5DpNPW4zkDKJOtCtiqtMLIkGm2gQiJea6jg5uSSR4yHHG3G9nFg9uTCS4tr29mN0DYENrK9ck\nk5xnLZ0cZJC9PMtufste7nxpiH+/6SYArr76Ak4+2dtUwbNn309Ly4UnnLZobFya87nMrojpTS+I\nlAoFAyIlJh6Ps7m/n13NzdRXVHDOwoXUV1Swq7k5MNsKcy1yHL2nHrvI8dJLL+Tkk28Fpr8lanIv\nsWDBl7nkkgvo6LiOROIWHOchxk9bPEQisZH29muPe7e1lnS6jOlML4iUkmLlGRCRGYjH45ntg52d\nWGsDsUZgVD6LHOfMmcOcOSfxhz9cC3yh4H0pL7+Ou+++kTlzMvUP+vs309Z2Mz09t5BOzyUWe5nG\nxlra23NvKxy/KyLXbzTx9IJIKVEwIFLignYhGrvIMffl8+giR2stJ520AHgdcBdwRcH6UVZ2F+ed\ndxrLlh2tfxCPx+nsXE9nJ1MOohoaaunq2pJdMzDeZNMLIqVE0wQiUnBjFzkmyewjvhpoBP4WODgy\nwtX/+I/ce9ddwEtAO/B9MgHBzJWV3UV9/ff5/OcnXj8x1SBqOtMLIqVGwYCIFNwn2tq44bTTWAp8\nnkxikX8Cvgk8Ajz5wgv806ZNzL3qKspffAZ4iEwKkkEyowPTXUPwEuXll3PxxYNs2nQHzgS7LvIR\nj8fp799Mc/MuKirqWbjwHCoq6mlu3qWshRIanqYjzpfSEYuUvscffZR/uewyPrJ/PxcePsycE7w+\nBbyPv+Bp7sTlbKAP+Bfgw8BFcMIjABxi9uz7WbDgy3zxi59i+XLvhu6DtkZDZNRM0hFrzYCIFITr\nurSuXs2BBx/kweFh5p34LQDEgV08Rxsf4RuUM+y8hpPm/JGq9zzEc899nd///u0MD9fiutXAYo7W\nOduL4wxQXt5HefkzXH31BVxyybdfXSxYSGMDAAUCEkYKBkRkxlzXZfX55/OerVv59MhI3u+PA50c\npJODWBe+QBnff81ivvvdh3n66afp63uSrVtvZe/eIVwXHAcWL66gvr6a2tqrSCQSBf+dVOFQokTT\nBCIyYzdceSWn33cfV0wjEJjIXWVlDF50Ef96550FO+ZUjaYgVoVDKSWBrVooIuH32COPMPzggwUN\nBACuGBnh+Qce4PFHHy3ocadCKYglahQMiMi0HTp0iHUf/zgbhoc9Of6G4WH+5bLLOHTI6/oF4ykF\nsUSNggERmbb777mHj+7fP+XFgvk6FfjIb37D1+6916MWjqcUxBJFCgZEZNq+dtttXHD4sKdtXPjK\nK9x/662etjHW+BTEuSgFsYSPggERmZZkMsnbDhyYUhaAmZgDvPXAAZLJpMctHTXdCocipUrBgIhM\ny67HHqP2hRd8aat2eJgn+/ybp1cKYokaBQMicpypzIcPbNtGtU/z5tWuy8DWrb60BUpBLNGjpEMi\nAmT21m9obaWvt5eydJqRWIzahgau6+jIefH75d69nO5T3xYDQ3v3+tRaxnQqHIqUKgUDIkIqlWJV\nTQ3XJJOsd91XE/5u6epi1Y4dbO7vPz4gyL7ODybbXrEoEJCw0zSBiLChtZVrkklWjrnAG2Cl67Im\nmeTmtrbj3+Q4E663LzSbbU9EvKFPl4jQ19vLignuvFe6Ln09Pcc9/ubFi9nndcey9gIVixf71JpI\n9CgYEIk4ay1l6fQkKXZgbjp93KLC6rPOYsCn4fMBx6G6vt6XtkSiSMGASMQZYxiJxSZJsQMjsdhx\n8+bvO/NM+l73Os/7B9BXXs57a2t9aUskihQMiAi1DQ1smWBO/mHHYWlj43GPJxIJnp4/H6+rBhwC\nfjF/vidlikUkQ8GAiHBdRwe3JBI8NGZRoAUechw2JhJc296e830XXH01Xzv5ZE/7dv/s2VzY0uJp\nGyJRp2BARIjH42zu72dXczP1FRWcs3Ah9RUV7Gpuzr2tMOvCSy/lSwsXctCjfr0EfHnBAi645BKP\nWhARUJ4BEcmKx+Os7+yEzs4pJ9mZM2cOn/riF7nu/PO5y4MyxteVl3Pj3XczZ47XFRBEos2zkQFj\nzP82xvQZY0aMMS961Y6IFF4+SXaWLl9O+Qc/yF1lZQXtw11lZZx23nnULltW0OOKyPG8nCaIAV8H\nPu9hGyISAB133MH36+sLFhDcVVbG9+vraf+8vj5E/OBZMGCt/T/W2k7gp161ISLB4DgOd2zaxOBF\nF3FFefm01xC8BFxeXs7gxRdzx6ZNOMo6KOILfdJEpCAcx+Ff77yTSzZt4oOnn87ds2dPedvhIeDu\n2bM57/TTuXTTJv71jjsUCIj4SJ82ESmopcuX8+2nnsJs3MgHEwlaTjuNrzkOe2DctsU9wNcch5bT\nTuO8d7wDs3Ej337qKZYuX168zotEVF67CYwxnwb+eZKXWCBhrf3FjHolIiVtzpw5XLp6NZeuXk0y\nmeTJvj5u3bo1U4bYdcFxqFi8mOr6eq6qrVVCIZEiM8fmG5/0xcbMB+af4GX7rLV/GvOeS4CN1trX\nTuH4VcDAsmXLmDdv3rjnmpqaaGpqmnJfRUREwqq7u5vu7u5xjx08eJCdO3cCVFtrd+dzvLyCgemY\nTjAwMDBAVVWVp/0SEREJk927d1NdXQ3TCAY8SzpkjFkEvBZ4MzDLGPPu7FN7rLUjXrUrIiIi+fEy\nA+GngI+O+f/RKOVvgZ0etisiIiJ58DLPwMestbNy/CgQEBERCRBtLRQREYk4BQMiEhheL2gWkdwU\nDIhIUaVSKda1tFBXWcm5ixZRV1nJupYWUqlUsbsmEhkqYSwiRZNKpVhVU8M1ySTrXRdDJnPZlq4u\nVu3Yweb+fuLxeLG7KRJ6GhkQkaLZ0NrKNckkK7OBAIABVroua5JJbm5rK2b3RCJDwYCIFE1fby8r\nXDfncytdl76eHp97JBJNCgZEpCistZSl06+OCBzLAHPTaS0qFPGBggERKQpjDCOxGBNd6i0wEoth\nzEThgogUioIBESmofO7kaxsa2OLk/hp62HFY2thYqG6JyCQUDIjIjE13e+B1HR3ckkjwkOO8OkJg\ngYcch42JBNe2t3vedxHR1kIRmaGZbA+Mx+Ns7u/n5rY2bunpYW46zcuxGLWNjWxub9e2QhGfKBgQ\nkRkZuz1w1Oj2QJvdHri+s3PC98fj8czznZ1Ya0t6jUCp91+iS9MEIjIjhdweWIoXUmVQlDDQyICI\nTFs+2wNL8UJ/IsqgKGGhkQERmbaobw9UBkUJCwUDIjIjUd4eqAyKEhYKBkRkRqK6PVAZFCVMFAyI\nyIyMbg/c1dxMfUUF5yxcSH1FBbuam0M9Zx71KRIJFy0gFJEZC9P2wHzUNjSwpatr3LbKUWGfIpFw\n0ciAiBRUVAIBiO4UiYSPggERkWmK6hSJhI+mCUREZiCqUyQSLhoZEBEpEAUCUqoUDIiIiEScggER\nEZGIUzAgIiIScQoGREREIk7BQEB1d3cXuwuBoXORofNwlM5Fhs7DUToXM+NZMGCMebMx5gvGmH3G\nmJeNMc8YY9YbY2JetRkm+sM+SuciQ+fhKJ2LDJ2Ho3QuZsbLPANvJ1Or4wpgL3AG8AVgLnC9h+2K\niIhIHjwLBqy1W4AtYx4aMsZsAFajYEBERCQw/F4zcCrwos9tioiIyCR8S0dsjFkCNAPXTPKy2QDJ\nZNKXPgXZwYMH2b17d7G7EQg6Fxk6D0fpXGToPBylczHu2jk73/caayeqxj3BG4z5NPDPk7zEAglr\n7S/GvGch8Aiww1r7PyY59oeBr+bVIRERERnrImvtffm8YTrBwHxg/glets9a+6fs6xcA/wE8Ya39\n2BSOvQIYAl7Jq2MiIiLRNhuoALZYaw/k88a8g4G8Dp4ZEdgBfB/4iPWyMREREZkWz4IBY8xfADvJ\n3OVfAhwZfc5a+ztPGhUREZG8ebmAsB44PfvzbPYxQ2ZNwSwP2xUREZE8eDpNICIiIsGn2gQiIiIR\np2BAREQk4gIbDBhj3mKM+YYx5gVjzEFjzGPGmOXF7lexGGP+wRjzvWzRpxeNMQ8Uu0/FYoz5M2PM\nj4wxrjHmXcXuj9+iXATMGPMJY8ygMeZQ9vPwnmL3yW/GmBuMMU8aY/5gjPmdMeZBY8xbi92vYsue\nF9cYc0ux+1IMxpgFxpgvG2OGs98LPzbGVE31/YENBoBvk1lo+DdAFfBj4NvGmNOK2aliMMasAr4E\n/L/AO4G/BvJKKBEy/wb8msxi1CgaWwTsHcAaMjU/OorZKa8ZYy4AbgbWAf+dzHfCFmNMeVE75r8z\ngduA9wF1QAzYaoyZU9ReFVE2KLyCzN9E5BhjTgX6gMNkcvUkgGuB30/5GEFcQJhNPvQCcKa1ti/7\n2CnAH4A6a+2OYvbPT8aYWWS2Z6611t5T3N4UnzHm74ENwCrgZ8BfWmt/UtxeFZ8x5jpgtbV2SbH7\n4hVjzPeAXdbaT2b/35DZqXSrtfbfitq5IsoGQ88Dy6y1jxe7P37LXhsGgKuAtcAPrbWTpb0PHWPM\nZ4Aaa+20R88DOTKQzZz0c+Cjxpi5xpiTyNz5/I7MP3qUVAELAIwxu40xvzHGfMcY844i98t3xpjX\nA/8OXAwcKnJ3gibURcCyUyDVwHdHH8smMdsO1BSrXwFxKplRstD++59AF9AbpZvEHBqAHxhjvp6d\nOtptjLk8nwMEMhjIOovMhTBF5ov/n4CV1tqDRe2V/04nMyS8DvgU8A9khn4ezQ4NRcndwO3W2h8W\nuyNBMqYI2B3F7ouHyslMGx6bsOx3wBv8704wZEdHPgs8bq39WbH74zdjzIXAXwI3FLsvRXY6mZGR\np8nk+LkDuNUYc/FUD+BrMGCM+XR2gcdEP0fGLIS5ncwHvRZ4D/AN4FvZu8OSl8e5GP03arfWfiN7\nIfwYmTuBfyzaL1AgUz0PxpgWIA7cNPrWInbbE3l+PkbfsxB4CPiatfaLxel5UY0mMouq28msG7mw\n2B3xmzHmjWQCoYutteli96fIHGDAWrvWWvtja+2/A3eRCRCmxNc1A1MtcgQsBx4GTrXWjox5/y+A\nL4RhfjCPc7GUTH2HpdbaJ8a8/3vANmvtWu966b0pnodB4OvA2cc8Pgv4E/DVExXBKgVT/ZuYThGw\nUpedJngZWGWt7Rnz+D3APGvtB4vVt2IxxnyOzPDwmdbaXxW7P34zxpwDPEAm1f3ozcEsMsHhEeDk\nqNTDMcYMAVuttVeOeWw10GqtXTSVY3iZjvg42bUAJ6ykNGZV7LH/kC7BntqYsjzOxQCZFaJvA57I\nPhYjU5nqlx520Rd5nIergdYxDy0AtgAfAp70pnf+muq5gOOKgF3mZb+CwFqbzn4WPgD0wKtD5B8A\nbi1m34ohGwicAyyPYiCQtZ3M7qqx7gGSwGeiEghk9ZG5Roz1NvK4RvgaDOShn8y8+L3GmBvJrBm4\nkswF8NtF7JfvrLUpY8wdwP8xxvyazD/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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10acd3f10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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0zJ49m3vu+RxFRetduX5R0XruvfcW12s6KH+ASIqCARGZluXLl3LJ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\nvVhKqr7DUmvt90e8/gfAXmvtze710n1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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ad27f10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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YRX8TZaRxhIMfPMhI4wjR56LU1Ge/jBo0meol2D+b+QyLqhZ6wIsn+WJ+wlaF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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ada8a10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ZDkXkRIL4uyvostVL+HLnl6d9Pa/zDFzq5fWDrK+nhw2TPMlv7O6GKU7rF3Md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\nlaebSqsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ae26f50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for it in range(max_its):\n",
    "    \n",
    "    \n",
    "    # Assign each point to its closest mean\n",
    "    # assignments are stored in z\n",
    "    \n",
    "    \n",
    "    # ADD CODE HERE\n",
    "    \n",
    "    # Plot the status of the algorithm\n",
    "    # The data are coloured according to the memberships in z\n",
    "    # and the means are plotted in the same colours with larger symbols\n",
    "    plt.figure()\n",
    "    for k in range(K):\n",
    "        plt.plot(x[z[:,k]==1,0],x[z[:,k]==1,1],cols[k])\n",
    "        plt.plot(mu[k,0],mu[k,1],cols[k],markersize=20)\n",
    "    \n",
    "    \n",
    "    # Check if anything has changes\n",
    "    changes = (np.abs(z - oldz)).sum()\n",
    "    if changes == 0:\n",
    "        break\n",
    "    # Update the means\n",
    "        \n",
    "    # ADD CODE HERE\n",
    "        \n",
    "    # Make a deep copy of z...\n",
    "    oldz = np.copy(z)\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
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